Toward Clemens' Conjecture in degrees between 10 and 24

Details Toward Clemens' Conjecture in degrees between 10 and 24 Toward Clemens' Conjecture in degrees between 10 and 24

1996-01-23

arxiv.org/abs/alg-geom/9601024v2

Mathematics

Algebraic Geometry

Plain Tex, This eleven page paper is a joint manuscript, produced in connection with the first author's participation in the c

Scientific paper

We introduce and study a likely condition that implies the following form of Clemens' conjecture in degrees $d$ between 10 and 24: given a general quintic threefold $F$ in complex $\IP^4$, the Hilbert scheme of rational, smooth and irreducible curves $C$ of degree $d$ on $F$ is finite, nonempty, and reduced; moreover, each $C$ is embedded in $F$ with balanced normal sheaf $\O(-1)\oplus\O(-1)$, and in $\IP^4$ with maximal rank.

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